Critical reaction to Interpol was generally positive. Aggregating website Metacritic notes that Interpol and Our Love to Admire which preceded it have served to establish a downward trend with regard to critical reception since their second release, Antics, although its rating of 66 out of 100 based on 33 reviews means it is still considered to have released to "generally favorable" reception.[14]AnyDecentMusic? shows a rating of 6.3 based on 33 reviews.[15] Victoria Segal of Q awarded the album four out of five stars, stating that "Paul Banks's vocals as attention-grabbing as a hand on the back of the neck while subtle textures rub up against the drama of the guitars" and concluded by saying that "for a band who specialise in the dark, their touch is thankfully light".[9] Chris Coplan from Consequence of Sound gave the album four stars out of five, praised the "rich narrative" and "brilliant pacing found throughout the record" and described it as "a story that builds from an emotionally-resilient semi-joyousness in the beginning [...] to creepy, morose, and sinister by the end".[16]Iann Robinson of CraveOnline described the album as "epic, sad, disastrously emotional music that is written to exploit feelings of melancholy and despair" and noticed that "with so much pop music either dedicated to false sentiments of love or infant bouts of angry tantrums it's kind of nice to hear a band looking into deeper ideas".[17] Simon Vozick-Levinson of Entertainment Weekly felt that on Interpol "the riffs [...] are grander, the rhythms more limber, and the melodies more memorably moody than they've been in years" and stated that "lapsed fans may be surprised to find themselves reminded of why they loved this band in the first place".[4] Rob Sheffield of Rolling Stone called it "a surprisingly solid comeback" and praised Daniel Kessler's guitar as "the essence of arty post-punk romance".[10] In an early track-by-track review of the album, Paul Stokes of NME wrote that the band is "as atmospheric and dark as they were on their debut, and yet more intricate, and - as the trumpets prove - orchestral".[18] Later, Mark Robinson of the same magazine gave the album six out of ten and said it "Interpol seems cinematic, abstract and complex, but that adds up to something interesting rather than thrilling."[19]

Luke John Winkie of No Ripcord gave it eight stars out of ten and thought that the band deserved "a significant amount of respect for taking the risk and mustering the sheer talent to create something so deeply submerged in melancholia you can't even see light."[20] Brett Uddenberg of URB gave the album four stars out of five and stated: "Banks leads his dark orchestra with aplomb on Interpol's most cohesive effort since Turn On The Bright Lights."[21] Mikael Wood of The Village Voice gave it a favorable review and said that Interpol "manage the seemingly unmanageable task of finding new wrinkles in a tightly defined sound, one that's been theirs for nearly a decade."[22] Justin Jacobs of Paste gave the album a score of 7.3 out of ten and stated, "Though the record meanders into aimless moping in its final third, most of the 10 tracks are bold, heavy and among Interpol's best."[23] Jim Scott of Under the Radar gave it seven stars out of ten and said that the album "restores some of the shine, but the music still feels softer somehow, the cuts not as precise."[24] Ian Wade of BBC Music also gave it a positive review and stated: "There's still the chance that this album will finally push [Interpol] into the stratosphere -- you wish Interpol were globally huge, you really do -- although it's likely that their future won't be written until after Dengler's tour-replacements have helped broaden the band's palette more."[25]

Other reviews are average or mixed: Yahoo! Music UK gave the album six stars out of ten and said that "Instead of ending tensely and dramatically [Interpol] are the final whimper and sigh of an album named after a band that have lost their way and aren't sure which direction they should be heading."[26]Alternative Press also gave the album three stars out of five and said, "Even if Banks sticks to the "I've got two secrets but I only told you one" songwriting approach, hopefully a band shakeup will spark the soulfulness only occasionally heard in his contributions."[26] Will Dean of The Guardian also gave it three stars out of five and said that "It could be that [Interpol are] distracted -- they've been together 10 years, and have numerous solo projects; is there more to for them to do with Interpol?"[27] Jamil Ahmad of musicOMH likewise gave the album three out of five stars and said, "Interpol mostly deliver on this album with what they do best, sprinkling some of their most creative moments across it. If this is a schism, it'll be intriguing to see what happens when the pieces eventually do settle."[28] Blake Solomon of AbsolutePunk gave the album a score of 56% and stated: "Even though I'm sad this record has left no lasting effect, I'm also happy that it might mean my life is heading somewhere positive."[29]Billboard gave it a mixed review and called it "undoubtedly a solid effort, but solid shouldn't be satisfying for a band that has proved to possess the talent of indie rock's elite class."[30] Paul Schrodt of Slant Magazine gave the album two-and-a-half stars out of five and said that it "may not be quite self-parody, but it's also not the sort of thing that's going to make [the band] hip again anytime soon. Not that they would even care."[31]

Benjamin Boles from NOW gave the album three stars out of five, saying that the band does not sound "exactly eclectic in mood, sound or even tempo" and noticing that "the best moments come when they shy away from their trademark wall-of-reverb blueprint". He concluded by saying that "it’s a better album than their last, and diehard fans should be satisfied, but it’s not going to get the rest [...] very excited".[32] Josh Modell of Spin gave the album a score of five out of ten and found it "more dull than hypnotic". He felt that "it tries to assemble skyscrapers, but ends up muddling around without a strong foundation" and noticed that Interpol sounds "both strangely distant and overly familiar, like a band struggling to remember who they are".[11] James Reed of The Boston Globe gave the album a mixed review and said that most songs have "room to ramble but nothing resembling a core" and called it "heady and disorienting".[33]Greg Kot of the Chicago Tribune gave the album two stars out of four, described it as "bits and pieces of promising music without strong foundations", and stated that although "the band sounds terrific", the album does not offer "more than one or two truly memorable songs".[34]